HW5 ENME382 S10 Section0201 solution

HW5 ENME382 S10 Section0201 solution - 5.12 Some...

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5.12 Some hypothetical alloy is composed of 25 wt% of metal A and 75 wt% of metal B. If the densities of metals A and B are 6.17 and 8.00 g/cm 3 , respectively, whereas their respective atomic weights are 171.3 and 162.0 g/mol, determine whether the crystal structure for this alloy is simple cubic, face- centered cubic, or body-centered cubic. Assume a unit cell edge length of 0.332 nm. Solution In order to solve this problem it is necessary to employ Equation 3.5; in this expression density and atomic weight will be averages for the alloy—that is ρ ave = nA ave V C N A Inasmuch as for each of the possible crystal structures, the unit cell is cubic, then V C = a 3 , or ρ ave = nA ave a 3 N A And, in order to determine the crystal structure it is necessary to solve for n , the number of atoms per unit cell. For n =1, the crystal structure is simple cubic, whereas for n values of 2 and 4, the crystal structure will be either BCC or FCC, respectively. When we solve the above expression for n the result is as follows: n = ρ ave a 3 N A A ave Expressions for A ave and ρ ave are found in Equations 5.14a and 5.13a, respectively, which, when incorporated into the above expression yields n = 100 C A ρ A + C B ρ B a 3 N A 100 C A A A + C B A B

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Substitution of the concentration values (i.e.,
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HW5 ENME382 S10 Section0201 solution - 5.12 Some...

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